Problems
At Taeyang’s uncle’s house in the countryside, there is a large melon field.
Taeyang became curious about how many melons are growing in the field. After thinking carefully, he came up with a good idea:
Eureka!
Count the number of melons growing in 1㎡ of area, then calculate the total area of the field. Using proportional reasoning, he can find the total number of melons.
The melon field is in a hexagonal shape shaped like an “L” or rotated 90°, 180°, or 270° (┏,ㄱ,┛ shapes).
All sides of the field are aligned either horizontally or vertically.
Starting from a corner, he measured the lengths of all six sides while walking along the perimeter of the field in counterclockwise order.
For example, if the field has the following shape:
Directions: right = east, left = west, down = south, up = north.
Starting from the top-left corner, moving counterclockwise along the perimeter: south 30 m, east 60 m, south 20 m, east 100 m, north 50 m, west 160 m.
The area of this field is 6800㎡. If there are 7 melons per 1㎡, then the total number of melons is 47600.
Input
The first line contains a positive integer K (1 ≤ K ≤ 20), the number of melons per 1㎡.
The next 6 lines each contain two integers representing the direction and length of each side, in order, starting from an arbitrary vertex and moving counterclockwise along the perimeter.
Directions are encoded as:
1 = east
2 = west
3 = south
4 = north
Lengths are integers between 1 and 500.
Output
Print a single integer: the total number of melons in the field.
Example
7
4 50
2 160
3 30
1 60
3 20
1 100
47600
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